Modelling molecular interaction pathways using a two-stage identification algorithm

In systems biology, molecular interactions are typically modelled using white-box methods, usually based on mass action kinetics. Unfortunately, problems with dimensionality can arise when the number of molecular species in the system is very large, which makes the system modelling and behavior simulation extremely difficult or computationally too expensive. As an alternative, this paper investigates the identification of two molecular interaction pathways using a black-box approach. This type of method creates a simple linear-in-the-parameters model using regression of data, where the output of the model at any time is a function of previous system states of interest. One of the main objectives in building black-box models is to produce an optimal sparse nonlinear one to effectively represent the system behavior. In this paper, it is achieved by applying an efficient iterative approach, where the terms in the regression model are selected and refined using a forward and backward subset selection algorithm. The method is applied to model identification for the MAPK signal transduction pathway and the Brusselator using noisy data of different sizes. Simulation results confirm the efficacy of the black-box modelling method which offers an alternative to the computationally expensive conventional approach

On Stability and Equilibria of Analog Feedback Networks

Both the analog Hopfield network [1] and the cellular neural network [2], [3] are special cases of the new M-lattice system, recently introduced to the signal processing community [4], [5], [6]. We prove that a subclass of the M-lattice is totally stable. This result also applies to the cellular neural network as a rigorous proof of its total stability. By analyzing the stability of fixed points, we derive the conditions for driving the equilibrium outputs of another subclass of the M-lattice to binary values. For the cellular neural network, this analysis is a precise formulation of an earlier argument based on circuit diagrams [2]. And for certain special cases of the analog Hopfield network, this analysis explains why the output variables converge to binary values even with non-zero neuron auto-connections. This behavior, observed in computer simulation by researchers for quite some time, is explained for the first time here. 1 Introduction The neurally-inspired network, introduced..